Title: Application of Real-Time Scheduling Techniques to Agent-Based Distributed Production Systems
1Application of Real-Time Scheduling Techniques
to Agent-Based Distributed Production Systems
2Goals
- Novel application area of RT Systems
- Put the RT scheduling theory into Production
Control System practical applications - Allow predictable aperiodic scheduling in the
presence of periodic tasks in a production stage
and shift of a PCS
3Overview
- Main focuses
- Taxonomy of multiprocessor platforms
- Parallel uniform platforms Why?
- Comparative study of relevant RT Multiprocessor
Scheduling Algorithms - Resource augmentation technique
- System characteristics
- TBS on uniform multiprocessors
- Schedulability analysis
- Example
- Performance evaluation
4Main focuses
- structure and present a methodology of a
manufacturing system under RT-Contraints - thorougly examine and compare the literature of
real-time scheduling theory and its application
to Production Control Systems - Present a firm real-time scheduling technique of
a distributed production control system - to develop predictable computational methods for
studying the aperiodic scheduling problem in uni-
and multiprocessor manufacturing systems under
real-time constraints.
5Workload considerations in a traditional PCS
Raw material
Product
Parts
Parts
Parts
Assembly
Galvanic
Machining
Broaching
Parallel uniform machines
Parallel uniform machines
Parallel uniform machines
Parallel uniform machines
Pre-planned production of parts realized by
traditional production planning and control
systems
6Workload considerations in a RT- PCS
Raw material
Product
Parts
Parts
Parts
Assembly
Galvanic
Machining
Broaching
Parallel uniform machines
Parallel uniform machines
Parallel uniform machines
Parallel uniform machines
Periodic and aperiodic production of parts in a
production system underlying real-time constraints
7Taxonomy of multiprocessor platforms
- Parallel identical machines Same task
production time for all machines - Parallel uniform machines Machines differ in
their production time, but production time does
not depend from the type of the task - Parallel unrelated machines The production time
of the machine depends from the type of the task.
8Parallel uniform platforms Why?
- give production system designers the possibility
to use machines with different production speeds - Need for machines with lower production capacity
to execute non-real-time or aperiodic tasks - Need for upgrade of some machines
9Comparative study of relevant RT Multiprocessor
Scheduling Algorithms
10Resource Augmentation technique
- Philipps et al. (1997)
- Preemptive identical multiprocessor
setting. -
- Several on-line algorithms that prove poor
performance from - an absolute worst-case perspective, are
optimal when allowed - moderately more resources.
- Funk et al. (2001)
- extended this method to be applied upon
uniform parallel - machines.
- However, their results apply only to
periodic tasks! -
11System characteristics
- ? s1, s2, s3, ..., sm / m ? ? and sj? sj1
for all j, 1 ? jlt m - m-machine uniform multiprocessor platform with
speeds or production capacities s1, s2, s3, ...,
smrespectively. - ? ?i,j / i,j ? ? A set of periodic tasks
with hard deadlines - J Ji,j / i,j ? ? A set of hard aperiodic
tasks ordered by increasing deadlines - Each job is characterized by arrival time ri ,
production time ci, deadline di, period pi. - ui ci / pi is the utilization of a task. The
tasks in ? and J are indexed according to a
decreasing utilization - Job preemption is permitted. O Oj,m / i ? ?
changeover time caused by the arrival of part
from type j at the machine m. - Job parallelism is forbidden.
12TBS on uniform multiprocessors
- Advantages on uniprocessor platforms
- good performance
- low memory capacity
- low implementation complexity
better maintainability - low computational complexity
less changeover time - overheads
- Rules
- 1. No machine is idled while there is an active
job awaiting - execution
- 2. When fewer than m jobs are active, they are
executed upon - the fastest machines while the slowest are
idled - 3. Higher priority jobs are executed on faster
processors - 4. When the jth aperiodic request arrives at
time trj - Cj 2Oj,m
- dj rj
- Us
-
13 TBS on uniform multiprocessors
- Definition (Funk et al.)
- m
- ? sk
- kj1
- ?? max ______
- Sj
- measures the degree by which ? differs from an
identical multiprocessor platform. - Speed of processors differ from each other
?? becomes smaller.
14 TBS on uniform multiprocessors
- Lemma 1. (Funk et al.)
- If the following condition is satisfied
- Sm ? ??. s1 Sm
- then for any set of jobs I and at any
time-instant t ?0 - W(A, ?,I,t) ? W(A, ?,I,t)
- Condition expresses the additional production
capacity needed by ? in terms of the parameter
?? and the speed of the fastest processor in ? - the smaller the value of ??, the more ?
deviates from being an identical multiprocessor,
the smaller the amount of this excessing
processing power needed.
15 TBS on uniform multiprocessors
Theorem 1. If the condition of Lemma 1 is
satisfied Sm ? ??. s1 Sm then I will
meet all deadlines when scheduled using TBS
algorithm executing on ?.
16Schedulability Analysis
Theorem 2 Given a set of n periodic tasks with
machine utilization Up and a TBS with machine
utilization Us, the whole set is feasibly
scheduled upon a multiprocessor platform if and
only if Up Us ? Sm where Up Up1 Up2
... Upm Theorem 3 (Funk et al) A periodic
task system ? will meet all deadlines when
scheduled on ? Sm ? ?? maxu1,Up/m Up
17Schedulability Analysis
Theorem 4 ... Sm ?? u1 Up Us The
aperiodic task system J has a utilization Us
Sm - ?? u1 - Up
18Example
- Consider a task system ? comprised of five
periodic tasks (ci,pi) - ? (15,10) , (4,5) , (14,20) , (6,15) , (2,10)
- and an aperiodic task (ri,ci)
- J (5,3)
- to be TBS scheduled upon the uniform
multiprocessor platform - ? 3,1,0.5. Will all deadlines be met?
- By definition ?? max (10.5)/3, 0.5/1 0.5
- By (Funk et al.) ? is feasible on some
3-processor multiprocessor platform having a
total computing capacity - 1,50,80,70,40,23,6
- and with the fastest processor having a computing
capacity s1u11,5 - By Theorem 4, we obtain Us0,15
- djmax5,0(3/0.15)35
19Performance Evaluation
20Performance Evaluation
21Performance Evaluation